I REALLY liked the Inbox app they made for gmail. Sadly, like all the best things google makes, it went the way of the dinosaurs.

You can add an outlook account to the gmail app. You may have to add it as Microsoft exchange instead of a regular Outlook account though, but the process is the same.

I suggest you use Outlook Lite instead of the normal Outlook. It's a lot lighter and will not prompt you to add any MDM profiles if your institution set any up

Also Gmail, because the spam filtering is great.

I keep a copy in Thunderbird though, just in case my account 'goes away' somehow.